Mackay claims 'inaccurate'
Malky Mackay is "very concerned about seriously inaccurate and misleading reports" in the media and will fully co-operate with any Football Association investigation.
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However, the League Managers' Association has said text messages sent during Mackay's employment at Cardiff were "regrettable".
The LMA issued a statement after it was confirmed that the Football Association were investigating a dossier sent to them by Cardiff reporting sexist, racist and homophobic comments by the former Bluebirds boss and the club's head of recruitment Iain Moody.
The statement read: "In the course of a search by the club in early 2014 of 10,000 private text messages sent to and from another member of staff during Mr Mackay's employment at Cardiff, in relation to other matters, it emerged that Malky had, it seems, sent a couple of one-line texts that were, with the benefit of hindsight, very regrettable and disrespectful of other cultures.
"These were two text messages sent in private at a time Malky felt under great pressure and when he was letting off steam to a friend during some friendly text message banter.
"That said, Malky believes he could and should have conducted himself better on these two isolated occasions. The precise details need to remain private for the time being until any FA process is complete."
"The LMA does not condone in any way any potential breach of equal-opportunities laws but would also point out that out of over 10,000 text messages and 70,000 documents produced over a long period of time it may not be a complete surprise that some inappropriate comments can sometimes be made by employees, like Malky, working under great pressure in highly-charged situations.
"If Malky has caused any offence by these two isolated matters he would, however, wish to sincerely apologise."
The dossier only came to light after Mackay, out of a job since leaving Cardiff, had been set to take over at Crystal Palace.
The statement added: "Malky finds it strange that these matters were only raised with the FA and in the media now, eight months after his employment ended and the day before he was reported as being offered the opportunity to become manager of Crystal Palace FC.
"Malky is also very concerned about seriously inaccurate and misleading reports of his alleged involvement in these matters in the media. It has never been alleged that he wrote any homophobic or sexist messages and he has confirmed that he did not do so.
"Further, there are incorrect and damaging suggestions that he sent a whole host of offensive and unpleasant messages that are simply not true and which give a grossly distorted and unfair view of Malky’s involvement in this matter. Malky looks forward to matters being put straight in due course, following any investigation of this matter.
"Malky cannot of course comment on the nature of any conduct or communications alleged to have been made by others.
"Malky has said that he will be fully co-operating with any FA investigation and that he looks forward to putting the record straight thereafter."
Mackay's representatives were unavailable for comment.
The Gay Football Supporters' Network (GFSN) admitted shock at the reports of Mackay's alleged homophobic comments.
"The GFSN is saddened to hear reports of alleged homophobic comments by Malky Mackay," said spokesman Simon Smith.
"Homophobia is still a problem in football and we expect a high standard of conduct from managers, who should be setting a positive example of inclusion.
"We will be following the story closely and asking the FA to fully investigate the allegations."
Earlier in the day, Moody resigned as sporting director of Crystal Palace.
A statement from Palace on Thursday morning read: "In light of the events of yesterday, sporting director Iain Moody has tendered his resignation and it has been accepted with immediate effect.
"There will be no further comment from the club on this matter."
Meanwhile, Kick It Out chairman Lord Herman Ouseley urged the FA not to hold back with any sanctions should the allegations against Mackay and Moody be proven.
"Kick It Out is aware but not shocked to hear of reports revealing alleged racist, anti-Semitic, sexist and homophobic comments made by former Cardiff City manager Malky Mackay, and Iain Moody, the current sporting director at Crystal Palace," said Lord Ouseley.
"The governing bodies and the clubs must denounce such attitudes prevalent in the game, and take the appropriate action.
"If these types of exchanges made privately make it into the public eye, the individuals concerned must accept the full consequences of their actions. Kick It Out now awaits the outcome of the Football Association's investigation.
"These revelations are further confirmation of how football is tainted with racism, sexism, homophobia and anti-Semitism, and the culture which continues to exist throughout the game and in wider society as a whole.
"The reality is that these views are most dangerously held by those people in positions of power, and the football establishment knows and condones it.
"What you see at face value is not always reflective of the attitudes which are actually held deep down.
"It's easy to present yourself as being reasonable and fair, and to behave in ways that hide prejudice and bias.
"However, any in-depth forensic examination or analysis of hidden views would be likely to reveal otherwise. That is what makes it difficult to eliminate and eradicate such prejudices, bigotry and even hatred.
"This familiar scenario acts as a challenge to the leadership of football that cannot be shirked again."